br: add integration test for ingest corner case test (#52734)

[ti-chi-bot]

This is an automated cherry-pick of #52734

What problem does this PR solve?

Issue Number: close #52733

Problem Summary:
When creating index, log backup should be able to start.

What changed and how does it work?

remove the check, and add integration test.

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No need to test

  • I checked and no code files have been changed.

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Documentation

• Affects user behaviors
• Contains syntax changes
• Contains variable changes
• Contains experimental features
• Changes MySQL compatibility

Release note

Please refer to Release Notes Language Style Guide to write a quality release note.

None

[ti-chi-bot]

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[Benjamin2037]

LGTM

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: Benjamin2037, BornChanger, jebter

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Needs approval from an approver in each of these files:

• OWNERS [Benjamin2037]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-04-19 09:53:10.107283022 +0000 UTC m=+591009.218329463: ☑️ agreed by BornChanger.
• 2024-04-19 10:06:39.272798267 +0000 UTC m=+591818.383844713: ☑️ agreed by Benjamin2037.

[Leavrth]

/test pull-br-integration-test

[tiprow]

@Leavrth: No presubmit jobs available for pingcap/tidb@release-7.1

In response to this:

/test pull-br-integration-test

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[codecov]

Codecov Report

❗ No coverage uploaded for pull request base (release-7.1@b1e0241). Click here to learn what that means.
The diff coverage is 0.0000%.

Additional details and impacted files

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